Estimating \(z_c\)  requires the variational inference [1]}, where the probability distribution \(p(z_c)\)  is assumed to be priorly defined, such as a zero-mean unit-variance Gaussian distribution. Taking the modeling of the prior distribution \(p(c)\)  for example, we can use following approximation:
\(\hspace{-3.1298pt}\begin{aligned}&\log p_{\vartheta , \phi }(c) = \log \int _{z_c} p_{\vartheta }(c |z_c) p(z_c) d z_c\\&\ge {\mathbb {E}}_{[z_c \sim q_{\phi }(z_c | c)]}[\log p_{\vartheta }(c | z_c)]-\text{KL}(q_{\phi }(z_c | c) \Vert  p(z_c))\end{aligned}\hspace{-4.2679pt}\) 
